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This programme looks how mathematical modelling can be applied to the cooking of a turkey.
Module code and title: M101, Mathematics: a foundation course M101; 23; 1986 27-07-1986 1986 00:24:18 + Show more... David Saunders Mike Crampin; Mike Simpson; Anne Walton BBC Open University Cooking time; Mathematical modelling; Turkey For how long should you cook a turkey? "Until the meat is tender and any harmful bacteria have been killed" is one answer. However, if you want the turkey to be ready at one o'clock then it's not a very helpful answer. You need to know in advance so that you can put the bird in the oven at an appropriate time, So what does the cooking time depend on? Is there a mathematical formula you could use to predict the cooking time for a range of different turkeys? Using mathematics to represent problems from real life is a part of the process called "Mathematical Modelling", the subject of Block V of the Mathematics Foundation Course M101. This television programme, the first in the block, uses the particular procedure for mathematical modelling. The programme's presenters set up a model and introduce suitable variables: in this case, the cooking time is assumed to be a function of the turkey's weight. To determine the nature of this function, they collect some experimental data by cooking several turkeys of varying weights until the internal temperature reaches a predetermined level; the data points seem to lie approximately on a straight line, suggesting a linear function. However, common sense says that the line should pass through the origin: a zero weight turkey should be cooked in no time at all: and closer examination of the data points suggests that two straight lines might give a better fit, and a curve might give a better fit still. Fitting a curve to data points is a technique introduced in the accompanying correspondence text when the curve is a simple power law and this technique: the use of a log-log plot: gives a two-thirds power law for the relationship between cooking time and weight. The lessons drawn from this attempt to solve the problem is that a systematic procedure is a help: in the programme, such a procedure is shown diagrammatically: and that several attempts may be needed to refine the model before an acceptable solution is obtained. HOU5289 FOUM239X 2484 no